Bar torsion

The bars torsion is one of the simplest Ressort S. If we neglect the ends, its active part is a bar full with diameter D and length L, or a tube of internal diameter d_i and external diameter d_e.

One of the ends of the bar is embedded and regarded as fixed, the other, known as free, is connected to the variable components.

The essential application of the torsion bars is the suspension of the vehicles, particularly of those of which the wheels are independent. One uses them not only on light vehicles, but also on machines of important mass (Tank for example) and much of cross-country vehicles.

Let us call M_t the torque applied at the loose lead of the bar and α the angle whose this end compared to the other turns, under the effect of this moment.

Condition of resistance

The maximum constraint of shearing in the spring is worth:

$\ tau= \ frac {MT} {\ frac {I_0} {V}} \ Leq {\ tau} _ {adm}$

with $\ tau = \ frac {16 \, MT} {\ pi d^3}$ (bars full)

or $\ tau = \ frac {16 \, d_e \, MT} {\ pi (d_e^4-d_i^4)}$ (tube)

Condition of deformation

The swing angle of the loose lead is worth:

$\ alpha= \ frac {MT \, L} {G \, I_o}$

with $\ alpha= \ frac {32 \, MT \, L} {\ pi \, G \, d^4}$ (bars full)

or $\ alpha= \ frac {32 \, MT \, L} {\ pi \, G \, (d_e^4-d_i^4)}$ (tube)

The stiffness is worth $k= \ frac {MT} {\ alpha} = \ frac {G \, I_o} {L}$

We will note that the unknown factors are easy to obtain starting from the formulas: indeed, for a given material, the diameters of the bar or tube are fixed by the condition of resistance, then the condition of deformation imposes the length.

Practical problems

In the torsion bars to circular section, the delicate problems are that of the fasteners, on the level of which one should not cause Concentration stresses. Generally, a cone of half point angle close to 30°, connected to the bar by broad a Fillet (ray R ~ 1,5.d), allows the increase in diameter necessary to the realization of the Cannelure S which will be committed in the female parts of the parts of connection. The stress concentration due to the change of ray will be weak, on the other hand the grooves ensuring the transmission of couple will give a coefficient of concentration stress neighbor of 2.

Let us note the possibility of associating a bar and a tube of torsion in order to decrease the length (suspension known as “DUBONNET”). It should be noted that a spring of torsion made of a tube will have a state of stress tending towards a uniform field, therefore will be of minimal volume. On the other hand, an elementary calculation gives the cylinder of cross-section minimal length.

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